Give the wetland a proper time block
Bharatpur makes sense when you have most of the day and birding is the main stop. It is less useful if you need a fast hotel transfer or are trying to fit several monuments and a flight into the same day.
Arrange the park visit separately from the car
A road driver, naturalist, park ticket and cycle-rickshaw are separate parts of the plan. Confirm each item and ask which park routes suit your mobility and interest. Leave camera equipment and valuables with you.
Set a cut-off time for leaving the park
Work back from your Jaipur arrival goal and account for road conditions. Keep lunch flexible, agree how luggage is handled, and do not book around a specific species or guaranteed wildlife sighting.